Acoustic metamaterials-driven transdermal drug delivery for rapid and on-demand management of acute disease

Transdermal drug delivery provides convenient and pain-free self-administration for personalized therapy. However, challenges remain in treating acute diseases mainly due to their inability to timely administrate therapeutics and precisely regulate pharmacokinetics within a short time window. Here we report the development of active acoustic metamaterials-driven transdermal drug delivery for rapid and on-demand acute disease management. Through the integration of active acoustic metamaterials, a compact therapeutic patch is integrated for penetration of skin stratum corneum and active percutaneous transport of therapeutics with precise control of dose and rate over time. Moreover, the patch device quantitatively regulates the dosage and release kinetics of therapeutics and achieves better delivery performance in vivo than through subcutaneous injection. As a proof-of-concept application, we show our method can reverse life-threatening acute allergic reactions in a female mouse model of anaphylaxis via a multi-burst delivery of epinephrine, showing better efficacy than a fixed dosage injection of epinephrine, which is the current gold standard ‘self-injectable epinephrine’ strategy. This innovative method may provide a promising means to manage acute disease for personalized medicine.


List of Contents Supplementary Methods
Theoretical prediction of acoustic metamaterials mediated drug release. Table  Table S1. Parameter list for simulation. Fig.S1 Design, device, and function of the acoustic metamaterial patches.

Supplementary Methods
Theoretical prediction of drug release mediated by acoustic metamaterials: The governing perturbation equations for acoustic fields in the porous media consist of a balance of linear momentum and mass. Considering the effects of the 2-phase porous metamaterial structure, the standard equation of porous medium dynamics can be written as 1 : The actual density of the fluid is , the volume fraction of porous media is , the interstitial fluid velocity is , ≡ 1/ is the inverse of the hydraulic conductivity , is the velocity of the porous solid frame, and is the relative velocity of the fluid. Under a harmonic force, the motion of the fluid is generally not harmonic. It is generally composed of two components: (1) a first-order component of the same period as the activation force, and (2) a second-order stable component (acoustic streaming). Taking the first and second-order components into account, we can write 2 : For the first-order equation, we assume that acoustic waves travel in a uniform media, and the fluid and porous frame move together with the same velocity. Thus, and 1 vanish in the firstorder equation, and we get: For the second-order equation, since there is no streaming in the porous frame, the second-order frame velocity is zero. Expanding the equation to the second order and averaging the equation over a cycle yields: The second-order equation has a form of Darcy's law, supplemented with a streaming force term. For the acoustically-enhanced convection-diffusion of dye and drug, the governing equation is the conventional diffusion equation 3 : c is the species concentration, D is the diffusivity, is the velocity field that the species is moving with. R describes sources or sinks of the quantity c.

S-3
Combining the second-order equation, we can get: Thus, the streaming speed in the porous media also has the estimated relation with acoustic pressure: ~2 �15� This streaming results in an effective diffusivity:

~2 �16�
If we simplify the convection-diffusion to 1D diffusion from the patch to the porous media, with a constant concentration 0 at the surface of the patch. We can get: 0 is the diffusivity of dye in the porous media. The regulation of this estimation equation is: Integrating along x to get (the total released dye mass) at time : To reduce the computational effort, we only solved for one pyramid in the periodic metamaterial structure in 3D, because the pyramidal structures' vibrations are periodic in both the x-and ydirections. Based on the above-discussed theoretical derivation, the numerical procedure is divided into three steps: (1) solving the acoustic field (1st-order problem) in the porous media domain; (2) solving the 2nd-order problem in a porous domain based on the 1st-order result from the first step and obtaining the streaming field; (3) solving for the diffusion of dye in porous domain assisted by acoustic streaming. COMSOL 5.3a (the COMSOL Group) was employed for the calculations following the above steps with all the parameters listed as shown in Table S1. A computational domain was used for simulating a unit of periodic metamaterial structures (Fig.S2a).
In step (1), the predefined "Pressure acoustics" modified with "Poroacoustics" physics was used to calculate the acoustic field distribution (1st-order problem) in porous media. A "Periodic" boundary condition, which confines periodic connection of pyramids in the array and fluidic S-4 domains, was applied to side the two boundaries of the porous domain. The top boundary was set as "normal impedance" equal to that of the porous media to eliminate wave reflection. An activation of defined periodicity was applied to the patch boundary to account for acoustic vibration. Based on these settings, a "Frequency Domain" solver was used to solve the abovementioned physics together at the driving frequency (1.01 MHz). In step (2), "Darcy's law" physics was used to solve the 2nd-order problem (Acoustic streaming) in porous media. The mass and force source terms were imposed by adding "weak contribution" and "volume force" conditions, respectively. Similarly, the condition, which confines periodic connection of pyramids in the array and fluidic domain, was applied to two surrounding boundaries. And an "outlet" boundary condition, which indicates no pressure difference on the two sides of a boundary, was imposed at the media-media interfaces. This physics is solved via a "Stationary" solver using the 1st-order solution of the previously mentioned "Frequency Domain" solver. As the last step, the "Transport of Diluted Species" was used to solve the diffusion problem of the dye. A constant concentration of dye is set on the surface of the patch to account for diffusion. All the walls of porous media were set as no flux boundary conditions. These physics were then solved via a "Time-Dependent" solver in a total of 1020 seconds with an interval of 0.1s by using the 2nd-order solution of the previously mentioned "Stationary" solver.  Table S1. Parameter list for simulation.